System Control and Rough Paths PDF Download
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Author: Terry Lyons
Publisher: Oxford University Press
ISBN: 9780198506485
Category : Mathematics
Languages : en
Pages : 358
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Book Description
This work describes a completely novel mathematical development which has already influenced probability theory, and has potential for application to engineering and to areas of pure mathematics: the evolution of complex non-linear systems subject to rough or rapidly fluctuating stimuli.
Author: Terry Lyons
Publisher: Oxford University Press
ISBN: 9780198506485
Category : Mathematics
Languages : en
Pages : 358
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Book Description
This work describes a completely novel mathematical development which has already influenced probability theory, and has potential for application to engineering and to areas of pure mathematics: the evolution of complex non-linear systems subject to rough or rapidly fluctuating stimuli.
Author: Peter K. Friz
Publisher: Springer Nature
ISBN: 3030415562
Category : Mathematics
Languages : en
Pages : 354
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Book Description
With many updates and additional exercises, the second edition of this book continues to provide readers with a gentle introduction to rough path analysis and regularity structures, theories that have yielded many new insights into the analysis of stochastic differential equations, and, most recently, stochastic partial differential equations. Rough path analysis provides the means for constructing a pathwise solution theory for stochastic differential equations which, in many respects, behaves like the theory of deterministic differential equations and permits a clean break between analytical and probabilistic arguments. Together with the theory of regularity structures, it forms a robust toolbox, allowing the recovery of many classical results without having to rely on specific probabilistic properties such as adaptedness or the martingale property. Essentially self-contained, this textbook puts the emphasis on ideas and short arguments, rather than aiming for the strongest possible statements. A typical reader will have been exposed to upper undergraduate analysis and probability courses, with little more than Itô-integration against Brownian motion required for most of the text. From the reviews of the first edition: "Can easily be used as a support for a graduate course ... Presents in an accessible way the unique point of view of two experts who themselves have largely contributed to the theory" - Fabrice Baudouin in the Mathematical Reviews "It is easy to base a graduate course on rough paths on this ... A researcher who carefully works her way through all of the exercises will have a very good impression of the current state of the art" - Nicolas Perkowski in Zentralblatt MATH
Author: Terry J. Lyons
Publisher: Springer
ISBN: 3540712852
Category : Mathematics
Languages : en
Pages : 126
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Book Description
Each year young mathematicians congregate in Saint Flour, France, and listen to extended lecture courses on new topics in Probability Theory. The goal of these notes, representing a course given by Terry Lyons in 2004, is to provide a straightforward and self supporting but minimalist account of the key results forming the foundation of the theory of rough paths.
Author: Karl Johan Åström
Publisher: Princeton University Press
ISBN: 069121347X
Category : Technology & Engineering
Languages : en
Pages : 523
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Book Description
The essential introduction to the principles and applications of feedback systems—now fully revised and expanded This textbook covers the mathematics needed to model, analyze, and design feedback systems. Now more user-friendly than ever, this revised and expanded edition of Feedback Systems is a one-volume resource for students and researchers in mathematics and engineering. It has applications across a range of disciplines that utilize feedback in physical, biological, information, and economic systems. Karl Åström and Richard Murray use techniques from physics, computer science, and operations research to introduce control-oriented modeling. They begin with state space tools for analysis and design, including stability of solutions, Lyapunov functions, reachability, state feedback observability, and estimators. The matrix exponential plays a central role in the analysis of linear control systems, allowing a concise development of many of the key concepts for this class of models. Åström and Murray then develop and explain tools in the frequency domain, including transfer functions, Nyquist analysis, PID control, frequency domain design, and robustness. Features a new chapter on design principles and tools, illustrating the types of problems that can be solved using feedback Includes a new chapter on fundamental limits and new material on the Routh-Hurwitz criterion and root locus plots Provides exercises at the end of every chapter Comes with an electronic solutions manual An ideal textbook for undergraduate and graduate students Indispensable for researchers seeking a self-contained resource on control theory
Author: Simo Särkkä
Publisher: Cambridge University Press
ISBN: 1316510085
Category : Business & Economics
Languages : en
Pages : 327
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Book Description
With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.
Author: Huaizhong Zhao
Publisher: World Scientific
ISBN: 9814360910
Category : Mathematics
Languages : en
Pages : 458
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Book Description
The volume is dedicated to Professor David Elworthy to celebrate his fundamental contribution and exceptional influence on stochastic analysis and related fields. Stochastic analysis has been profoundly developed as a vital fundamental research area in mathematics in recent decades. It has been discovered to have intrinsic connections with many other areas of mathematics such as partial differential equations, functional analysis, topology, differential geometry, dynamical systems, etc. Mathematicians developed many mathematical tools in stochastic analysis to understand and model random phenomena in physics, biology, finance, fluid, environment science, etc. This volume contains 12 comprehensive review/new articles written by world leading researchers (by invitation) and their collaborators. It covers stochastic analysis on manifolds, rough paths, Dirichlet forms, stochastic partial differential equations, stochastic dynamical systems, infinite dimensional analysis, stochastic flows, quantum stochastic analysis and stochastic Hamilton Jacobi theory. Articles contain cutting edge research methodology, results and ideas in relevant fields. They are of interest to research mathematicians and postgraduate students in stochastic analysis, probability, partial differential equations, dynamical systems, mathematical physics, as well as to physicists, financial mathematicians, engineers, etc.
Author: Eduardo D. Sontag
Publisher: Springer Science & Business Media
ISBN: 1461205778
Category : Mathematics
Languages : en
Pages : 543
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Book Description
Geared primarily to an audience consisting of mathematically advanced undergraduate or beginning graduate students, this text may additionally be used by engineering students interested in a rigorous, proof-oriented systems course that goes beyond the classical frequency-domain material and more applied courses. The minimal mathematical background required is a working knowledge of linear algebra and differential equations. The book covers what constitutes the common core of control theory and is unique in its emphasis on foundational aspects. While covering a wide range of topics written in a standard theorem/proof style, it also develops the necessary techniques from scratch. In this second edition, new chapters and sections have been added, dealing with time optimal control of linear systems, variational and numerical approaches to nonlinear control, nonlinear controllability via Lie-algebraic methods, and controllability of recurrent nets and of linear systems with bounded controls.
Author: Aude Billard
Publisher: MIT Press
ISBN: 0262367017
Category : Technology & Engineering
Languages : en
Pages : 425
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Book Description
Methods by which robots can learn control laws that enable real-time reactivity using dynamical systems; with applications and exercises. This book presents a wealth of machine learning techniques to make the control of robots more flexible and safe when interacting with humans. It introduces a set of control laws that enable reactivity using dynamical systems, a widely used method for solving motion-planning problems in robotics. These control approaches can replan in milliseconds to adapt to new environmental constraints and offer safe and compliant control of forces in contact. The techniques offer theoretical advantages, including convergence to a goal, non-penetration of obstacles, and passivity. The coverage of learning begins with low-level control parameters and progresses to higher-level competencies composed of combinations of skills. Learning for Adaptive and Reactive Robot Control is designed for graduate-level courses in robotics, with chapters that proceed from fundamentals to more advanced content. Techniques covered include learning from demonstration, optimization, and reinforcement learning, and using dynamical systems in learning control laws, trajectory planning, and methods for compliant and force control . Features for teaching in each chapter: applications, which range from arm manipulators to whole-body control of humanoid robots; pencil-and-paper and programming exercises; lecture videos, slides, and MATLAB code examples available on the author’s website . an eTextbook platform website offering protected material[EPS2] for instructors including solutions.
Author: J. Christopher Westland
Publisher: Springer
ISBN: 3319165070
Category : Technology & Engineering
Languages : en
Pages : 184
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Book Description
This compact reference surveys the full range of available structural equation modeling (SEM) methodologies. It reviews applications in a broad range of disciplines, particularly in the social sciences where many key concepts are not directly observable. This is the first book to present SEM’s development in its proper historical context–essential to understanding the application, strengths and weaknesses of each particular method. This book also surveys the emerging path and network approaches that complement and enhance SEM, and that will grow importance in the near future. SEM’s ability to accommodate unobservable theory constructs through latent variables is of significant importance to social scientists. Latent variable theory and application are comprehensively explained and methods are presented for extending their power, including guidelines for data preparation, sample size calculation and the special treatment of Likert scale data. Tables of software, methodologies and fit statistics provide a concise reference for any research program, helping assure that its conclusions are defensible and publishable.
Author: Abdenacer Makhlouf
Publisher: John Wiley & Sons
ISBN: 1789450187
Category : Mathematics
Languages : en
Pages : 338
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Book Description
This book is part of Algebra and Geometry, a subject within the SCIENCES collection published by ISTE and Wiley, and the second of three volumes specifically focusing on algebra and its applications. Algebra and Applications 2 centers on the increasing role played by combinatorial algebra and Hopf algebras, including an overview of the basic theories on non-associative algebras, operads and (combinatorial) Hopf algebras. The chapters are written by recognized experts in the field, providing insight into new trends, as well as a comprehensive introduction to the theory. The book incorporates self-contained surveys with the main results, applications and perspectives. The chapters in this volume cover a wide variety of algebraic structures and their related topics. Alongside the focal topic of combinatorial algebra and Hopf algebras, non-associative algebraic structures in iterated integrals, chronological calculus, differential equations, numerical methods, control theory, non-commutative symmetric functions, Lie series, descent algebras, Butcher groups, chronological algebras, Magnus expansions and Rota–Baxter algebras are explored. Algebra and Applications 2 is of great interest to graduate students and researchers. Each chapter combines some of the features of both a graduate level textbook and of research level surveys.
